Boundary-Layer Meteorology

, Volume 145, Issue 1, pp 249–272 | Cite as

Analytical and Numerical Investigation of Two-Dimensional Katabatic Flow Resulting from Local Surface Cooling

  • Alan Shapiro
  • Bryan Burkholder
  • Evgeni Fedorovich
Article

Abstract

The analysis of katabatic flows is often complicated by heterogeneity in surface characteristics. This study focuses on an idealized type of katabatic flow driven by a simple form of inhomogeneous surface forcing: a buoyancy or buoyancy flux that varies down the slope as a top-hat profile (cold strip). We consider the two-dimensional Boussinesq system of governing flow equations with the slope angle, Brunt–Väisälä frequency, and coefficients of eddy viscosity and diffusivity treated as constants. The steady-state problem is solved analytically in a linearized boundary-layer framework. Key flow structures are a primary katabatic jet (essentially the classical one-dimensional Prandtl jet), a rotor-like feature straddling the upslope end of the strip, and two nearly horizontal jets: an inward jet of environmental air feeding into the primary jet on the upslope end of the strip and an outward jet resulting from the intrusion of the primary katabatic jet into the environment on the downslope end of the strip. Next, the corresponding nonlinear initial value problem is solved numerically until a steady state is reached at low levels. The main features of the linear solution are seen in the numerical results, but with some notable differences: (i) the primary jet in the numerical simulation requires a longer distance to attain a one-dimensional boundary-layer structure and extends further downslope off the strip before intruding into the environment; (ii) the numerically simulated outward environmental jet is narrower and more intense than the inward jet, and has a pronounced wave-like structure.

Keywords

Buoyancy Buoyancy flux Inhomogeneous surface Katabatic flow Stable stratification 

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References

  1. Atkinson BW (1981) Meso-scale atmospheric circulations. Academic Press, LondonGoogle Scholar
  2. Axelsen SL, Shapiro A, Fedorovich E, van Dop H (2010) Analytical solution for katabatic flow induced by an isolated cold strip. Environ Fluid Mech 10: 387–414CrossRefGoogle Scholar
  3. Banta RM, Olivier LD, Gudiksen PH, Lange R (1996) Implications of small-scale flow features to modeling dispersion over complex terrain. J Appl Meteorol 35: 330–342CrossRefGoogle Scholar
  4. Banta RM, Shepson PB, Bottenheim JW, Anlauf KG, Wiebe HA, Gallant A, Biesenthal T, Olivier LD, Zhu C-J, McKendry IG, Steyn DG (1997) Nocturnal cleansing flows in a tributary valley. Atmos Environ 31: 2147–2162CrossRefGoogle Scholar
  5. Barros N, Borrego C, Toll I, Soriano C, Jiménez P, Baldasano JM (2003) Urban photochemical pollution in the Iberian peninsula: Lisbon and Barcelona airsheds. J Air Waste Manag Assoc 53: 347–359CrossRefGoogle Scholar
  6. Bossert JE (1997) An investigation of flow regimes affecting the Mexico City region. J Appl Meteorol 36: 119–140CrossRefGoogle Scholar
  7. Broder B, Gygax HA (1985) The influence of locally induced wind systems on the effectiveness of nocturnal dry deposition of ozone. Atmos Environ 19: 1627–1637CrossRefGoogle Scholar
  8. Burkholder B, Shapiro A, Fedorovich E (2009) Katabatic flow induced by a cross-slope band of surface cooling. Acta Geophys 57: 923–949CrossRefGoogle Scholar
  9. Clements WE, Archuleta JA, Hoard DE (1989) Mean structure of the nocturnal drainage flow in a deep valley. J Appl Meteorol 28: 457–462CrossRefGoogle Scholar
  10. Cox HJ (1920) Weather conditions and thermal belts in the North Carolina mountain region and their relation to fruit growing. Ann Assoc Am Geogr 10: 57–68Google Scholar
  11. Dickerson MH, Gudiksen PH (1983) Atmospheric studies in complex terrain. Technical progress report N-1979 through FY-1983Google Scholar
  12. Dunbar GS (1966) Thermal belts in North Carolina. Geogr Rev 56: 516–526CrossRefGoogle Scholar
  13. Egger J (1981) On the linear two-dimensional theory of thermally induced slope winds. Beitr Phys Atmos 54: 465–481Google Scholar
  14. Fedorovich E, Shapiro A (2009a) Structure of numerically simulated katabatic and anabatic flows along steep slopes. Acta Geophys 57: 981–1010CrossRefGoogle Scholar
  15. Fedorovich E, Shapiro A (2009b) Turbulent natural convection along a vertical plate immersed in a stably stratified fluid. J Fluid Mech 636: 41–57CrossRefGoogle Scholar
  16. Fedorovich E, Nieuwstadt FTM, Kaiser R (2001) Numerical and laboratory study of a horizontally evolving convective boundary layer. Part I: Transition regimes and development of the mixed layer. J Atmos Sci 58: 70–86Google Scholar
  17. Fernando HJS (2010) Fluid dynamics of urban atmospheres in complex terrain. Annu Rev Fluid Mech 42: 365–389CrossRefGoogle Scholar
  18. Fernando HJS, Lee SM, Anderson J, Princevac M, Pardyjak E, Grossman-Clarke S (2001) Urban fluid mechanics: air circulation and contaminant dispersion in cities. Environ Fluid Mech 1: 107–164CrossRefGoogle Scholar
  19. Finn D, Clawson KL, Carter RG, Rich JD, Allwine KJ (2008) Plume dispersion anomalies in a nocturnal urban boundary layer in complex terrain. J Appl Meteorol Climatol 47: 2857–2878CrossRefGoogle Scholar
  20. Gohm A, Harnisch F, Vergeiner J, Obleitner F, Schnitzhofer R, Hansel A, Fix A, Neininger B, Emeis S, Schäfer K (2009) Air pollution transport in an alpine valley: results from airborne and ground-based observations. Boundary-Layer Meteorol 131: 441–463CrossRefGoogle Scholar
  21. Grisogono B, Oerlemans J (2001) Katabatic flow: analytic solution for gradually varying eddy diffusivities. J Atmos Sci 58: 3349–3354CrossRefGoogle Scholar
  22. Haiden T (2003) On the pressure field in the slope wind layer. J Atmos Sci 60: 1632–1635CrossRefGoogle Scholar
  23. Hernández E, de las Parras J, Martín I, Rúa A, Gimeno L (1998) A field case study and numerical simulation of mountain flows with weak ambient winds. J Appl Meteorol 37: 623–637CrossRefGoogle Scholar
  24. Hootman BW, Blumen W (1983) Analysis of nighttime drainage winds in Boulder, Colorado during 1980. Mon Weather Rev 111: 1052–1061CrossRefGoogle Scholar
  25. Jeffrey DJ, Norman AC (2004) Not seeing the roots for the branches: multivalued functions in computer algebra. ACM SIGSAM Bull 38: 57–66CrossRefGoogle Scholar
  26. King JA, Shair FH, Reible DD (1987) The influence of atmospheric stability on pollutant transport by slope winds. Atmos Environ 21: 53–59CrossRefGoogle Scholar
  27. Kobayashi T, Mori M, Wakimizu K, Takeshita K (1994) An observational study of a thermal belt on hillsides. J Meteorol Soc Jpn 72: 387–399Google Scholar
  28. Koh RCY (1966) Viscous stratified flow toward a sink. J Fluid Mech 24: 555–575CrossRefGoogle Scholar
  29. Kondo H (1984) The difference of the slope wind between day and night. J Meteorol Soc Jpn 62: 224–233Google Scholar
  30. Kossmann M, Sturman A (2004) The surface wind field during winter smog nights in Christchurch and coastal Canterbury, New Zealand. Int J Climatol 24: 93–108CrossRefGoogle Scholar
  31. Lee SM, Fernando HJS, Princevac M, Zajic D, Sinesi M, McCulley JL, Anderson J (2003) Transport and diffusion of ozone in the nocturnal and morning planetary boundary layer of the Phoenix valley. Environ Fluid Mech 3: 331–362CrossRefGoogle Scholar
  32. Lehner M, Gohm A (2010) Idealised simulations of daytime pollution transport in a steep valley and its sensitivity to thermal stratification and surface albedo. Boundary-Layer Meteorol 134: 327–351CrossRefGoogle Scholar
  33. Low PS (1990) Katabatic winds in the lower Tamar valley, Tasmania. Il Nuovo Cimento C13: 981–994Google Scholar
  34. Lu R, Turco RP (1994) Air pollutant transport in a coastal environment. Part I: Two-dimensional simulations of sea-breeze and mountain effects. J Atmos Sci 51: 2285–2308CrossRefGoogle Scholar
  35. Mahrt L (1982) Momentum balance of gravity flows. J Atmos Sci 39: 2701–2711CrossRefGoogle Scholar
  36. Mahrt L, Larsen S (1982) Small scale drainage front. Tellus 34: 579–587CrossRefGoogle Scholar
  37. Mahrt L, Vickers D, Nakamura R, Soler MR, Sun J, Burns S, Lenschow DH (2001) Shallow drainage flows. Boundary-Layer Meteorol 101: 243–260CrossRefGoogle Scholar
  38. Mathews J, Walker RL (1970) Mathematical methods of physics. Benjamin/Cummings, Menlo ParkGoogle Scholar
  39. Millán MM, Estrela MJ, Badenas C (1998) Meteorological processes relevant to forest fire dynamics on the Spanish Mediterranean coast. J Appl Meteorol 37: 83–100CrossRefGoogle Scholar
  40. Monti P, Fernando HJS, Princevac M, Chan WC, Kowalewski TA, Pardyjak ER (2002) Observations of flow and turbulence in the nocturnal boundary layer over a slope. J Atmos Sci 59: 2513–2534CrossRefGoogle Scholar
  41. Nappo CJ, Shankar Rao K, Herwehe JA (1989) Pollutant transport and diffusion in katabatic flows. J Appl Meteorol 28: 617–625CrossRefGoogle Scholar
  42. Oerlemans J (1998) The atmospheric boundary layer over melting glaciers. In: Holtslag AAM, Duynkerke PG (eds) Clear and cloudy boundary layers. Royal Netherlands Academy of Arts and Sciences, Amsterdam, pp 129–153Google Scholar
  43. Papadopoulos KH, Helmis CG, Soilemes AT, Kalogiros J, Papageorgas PG, Asimakopoulos DN (1997) The structure of katabatic flows down a simple slope. Q J R Meteorol Soc 123: 1581–1601CrossRefGoogle Scholar
  44. Poulos G, Zhong S (2008) An observational history of small-scale katabatic winds in mid-latitudes. Geogr Compass 2: 1798–1821CrossRefGoogle Scholar
  45. Prandtl L (1942) Führer durch die Strömungslehre. Vieweg and Sohn, BraunschweigGoogle Scholar
  46. Segal M, Yu C-H, Arritt RW, Pielke RA (1988) On the impact of valley/ridge thermally induced circulations on regional pollutant transport. Atmos Environ 22: 471–486CrossRefGoogle Scholar
  47. Shapiro A, Fedorovich E (2004a) Unsteady convectively driven flow along a vertical plate immersed in a stably stratified fluid. J Fluid Mech 498: 333–352CrossRefGoogle Scholar
  48. Shapiro A, Fedorovich E (2004b) Prandtl number dependence of unsteady natural convection along a vertical plate in a stably stratified fluid. Int J Heat Mass Transf 47: 4911–4927CrossRefGoogle Scholar
  49. Shapiro A, Fedorovich E (2006) Natural convection in a stably stratified fluid along vertical plates and cylinders with temporally-periodic surface temperature variations. J Fluid Mech 546: 295–311CrossRefGoogle Scholar
  50. Shapiro A, Fedorovich E (2007) Katabatic flow along a differentially-cooled sloping surface. J Fluid Mech 571: 149–175CrossRefGoogle Scholar
  51. Shapiro A, Fedorovich E (2008) Coriolis effects in homogeneous and inhomogeneous katabatic flows. Q J R Meteorol Soc 134: 353–370CrossRefGoogle Scholar
  52. Sharples JJ (2009) An overview of mountain meteorological effects relevant to fire behaviour and bushfire risk. Int J Wildland Fire 18: 737–754CrossRefGoogle Scholar
  53. Soriano C, Baldasano JM, Buttler WT, Moore K (2001) Circulatory patterns of air pollutants within the Barcelona air basin in a summertime situation: lidar and numerical approaches. Boundary-Layer Meteorol 98: 33–55CrossRefGoogle Scholar
  54. Sturman AP (1987) Thermal influences on airflow in mountainous terrain. Prog Phys Geogr 11: 183–206CrossRefGoogle Scholar
  55. Sturman AP, McGowan HA, Spronken-Smith RA (1999) Mesoscale and local climates in New Zealand. Prog Phys Geogr 23: 611–635CrossRefGoogle Scholar
  56. Tanaka H, Tanimoto Y, Mikami T (1998) The relationship between double-thermal inversions and thermal belt in the Mt. Yatsugatake area, central Japan. Geographical reports of Tokyo Meteorological University 33, pp 21–31Google Scholar
  57. Tyson PD (1968) Velocity fluctuations in the mountain wind. J Atmos Sci 25: 381–384CrossRefGoogle Scholar
  58. Ueda H, Hori ME, Nohara D (2003) Observational study of the thermal belt on the slope of Mt. Tsukuba. J Meteorol Soc Jpn 81: 1283–1288CrossRefGoogle Scholar
  59. Vergeiner I, Dreiseitl E (1987) Valley winds and slope winds—observations and elementary thoughts. Meteorol Atmos Phys 36: 267–286Google Scholar
  60. Whiteman CD (1990) Observations of thermally developed wind systems in mountainous terrain. In: Atmospheric processes over complex terrain. Meteorol monograph no. 45. American Meteorological Society, pp 5–42Google Scholar
  61. Whiteman CD (2000) Mountain meteorology: fundamentals and applications. Oxford University Press, New YorkGoogle Scholar
  62. Yakovenko SN, Thomas TG, Castro IP (2011) A turbulent patch arising from a breaking internal wave. J Fluid Mech 677: 103–133CrossRefGoogle Scholar
  63. Yoshino MM (1984) Thermal belt and cold air drainage on the mountain slope and cold air lake in the basin at quiet, clear night. GeoJournal 8: 235–250CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Alan Shapiro
    • 1
    • 2
  • Bryan Burkholder
    • 1
  • Evgeni Fedorovich
    • 1
  1. 1.School of MeteorologyUniversity of OklahomaNormanUSA
  2. 2.Center for Analysis and Prediction of StormsUniversity of OklahomaNormanUSA

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